05C50 Online Seminar: Mahsa Shirazi

An interesting question in spectral graph theory is about the structure of the eigenvectors of matrices associated with graphs. A graph is weakly Hadamard diagonalizable (WHD) if its Laplacian matrix L can be diagonalized with a weakly Hadamard matrix. In other words, if L = PDP^{-1} , where D is a diagonal matrix and P has the property that all entries in P are from {0,-1,1} and that P^TP is a tridiagonal matrix. In this talk, I will present some necessary and sufficient conditions for a graph to be WHD. Some families of graphs whichare WHD will also be presented.

This work is part of a research project done with the discrete math research group (DMRG) at the University of Regina.